生物統(tǒng)計(jì)與試驗(yàn)設(shè) 第九章協(xié)方差分ysisofcovariance(ANOCOVA)isatechniquethatcombinesfeaturesofanysisofcovariance(ANOCOVA)isatechniquethatcombinesfeaturesofanalysisofvarianceandCovarianceisusedwhentheresponsevariabley,inadditiontobeingaffectedbythetreatments,butalsorelatedtoanothervariableItaugmentthe ysisofvariancemodelcontainingthefactoreffectswith more additional that relatedtothedependent多Itintendedtoreducethevarianceoftheerrortermsinthemodel.ANOCOVAutilizestherelationshipbetweenthedependentvariableandoneormoreindependent observationsareavailableinordertoreducetheerrortermvariabilityandmakethestudyamoreoneforcomparingtreatment

Eachindependent variableaddedtothestudyiscalleda itantvariable相伴變量Thechoice itantisanimportantIfsuchvariableshavenorelationtothedependentvariable,nothingistobegainedbycovarianc itantvariablesfrequentlyusedwithhumansubjectsincludepre-studyattitudes,age,IQ,and9.1Single-factor9.1Single-factorCovarianceCaseStudiedAcompanywishedtostudytheeffectsofthreedifferenttypesofpromotionsonsalesofitsTreatmentl:SamplingofproductbycustomersinstoreandregularshelfTreatment2:AdditionalshelfspaceinregularlocationTreatment3:SpecialdisplayshelvesatendsofaisleinadditiontoregularshelfEachstorewasrandomlyassignedoneofthepromotiontypes,withfivestoresassignedtoeachtypeofpromotion.Otherrelevantconditionsunderthecontrolofthecompany,suchaspriceandadvertising,werekeptthesameforallstoresinthestudy.duringthepromotionalperiod itantvariableX:salesofproductinthepreceding 生物統(tǒng)計(jì)與試驗(yàn)設(shè) 第九章協(xié)方差分TableofANOVATableforModelwithoutCovariate(Type MS(Adj)FvalueP- t- Error(,)t(r-1)=12ANOVATableforModelwithOneCovariate(Type MS(Adj)FvalueP-1t-Error(,,)t(r-1)-1=11

ysiswithoutY112233123123ysiswithOneYPr>112233123123 =+++ii=1,2,,a;j=1,2,,rDataCracker;InputTreatDoR=1to5;InputYX@;Note:thedataisinputinthedo…endloop,wheretheoutputmeansthatanobservationwillbeoutputduringeachloop224528382932293130211628;PROCClassMODELY=LsMeansTreat/STDERRPDIFFAdjust=Tukey;PROCClassMODELY=XLsMeansTreat/STDERRPDIFFAdjust=Tukey;DataInputTreat$PrePost@@;Trt1 100Trt1Trt1 Trt2Trt2 Trt2Trt3 Trt3Trt3 ;PROCClassMODELPost=LsMeansTreat/STDERRPDIFFPROCclassMODELPost=PreLsMeansTreat/STDERRPDIFFAdjust=Tukey;CaseStudiedCaseStudiedAstudyontheeffectsoftwotreatmentsandcontroltothelearning-disablechildren. 生物統(tǒng)計(jì)與試驗(yàn)設(shè) 第九章協(xié)方差分TableofANOVATableforModelwithoutCovariate(TypeIII)Sourcedf FvalueP-value 2432. Error6 ANOVATableforModelwithOneCovariate(TypeIII)Sourcedf FvalueP-valueX|,TT|,XError

ysiswithoutY112233123123ysiswithOneYPr>1122331231239.2MultifactorCovarianceTwo-factorFactorialinaRandomizedCompleteBlockDesignwithOneCovariableYijk=+Xijk+i+j+ij+k+ANOVATableforModelwithOneCovariate(TypeSourcdfSS(adjR(|,,,,1SSXR(|,,,,a-SSAR(|,,,,b-SSBR(|,,,,(a-1)(b-SSAR(|,,,,r-SSRErro(ab-1)(r-1)-SSEData

SASCaseStudyA flowervariety(factorA:LP,WB)andmoisturelevel(factorB:low,high)onyieldofsalableflowersCaseStudyA flowervariety(factorA:LP,WB)andmoisturelevel(factorB:low,high)onyieldofsalableflowersBecausetheplotswerenotofthesamesize,thehorticulturistwishedtouseplotsize(X)asSixreplicationsweremadeforeachtreatment.experimenttostudytheeffects;PROCClassABMODELY=XLsMeansAB/STDERRPDIFFAdjust=TukeyETYPE=3;LSMeansA*B/STDERRPDIFFAdjust=TukeyETYPE=3;TheETYPE=optionspecifiesthetype(1,2,3,or4,correspondingtoTypeI,II,III,andIVtests,respectively)oftheE=effect.IfyouspecifytheE=optionbutnottheETYPE=option,thehighesttypecomputedinthe ysisisused.IfyouomittheE=option,theETYPE=optionhasno TableofANOVATableforModelwithoutCovariateTableofANOVATableforModelwithoutCovariate(TypeIII)Source FvalueP-A|,B,AB1 B|,A,AB1AB|,A,B1 204114.000000ANOVATableforModelwithOneCovariate(TypeIII) SS(Adj) FvalueP-valueX|,A,B,AB13994.5188173994.518817635.21A|,B,AB,X196.60182696.601826 B|,A,AB,X132